The dynamic behavior of a pilot scale absorption process has been approximated by the transfer function model

$Y^{\text{'}}(s)=\frac{-0\mathrm{.}025}{(1\mathrm{.}5s+1)}{U}^{\text{'}}(s)$

Where $Y^{\text{'}}$ is the deviation of $S{O}_2$ concentration from its nominal operating value of $100$ ppm$,$ measured at the absorber$\text{'}$s outlet; and $U\text{'}$ is the absorber water flowrate in deviation from its nominal value of $250gpm$; time is in minutes. It is desired to design a PI controller for this process $($assuming for now that the dynamics of the sensor as well as those of the valve are negligible$)$ by assigning the closed$-$loop system poles to the same location as the roots of the quadratic equation:

$s^2+s+1=0$

Find the values of $K_c$ and $\frac{1}{{}_{\text{I}}}$ required to achieve this pole assignment. $[$Pay attention to the sign of $K_c$ must have, for the controller's action to be reasonable.$]$